RSA加解密中必须考虑到的密钥长度、明文长度和密文长度问题。明文长度需要小于密钥长度，而密文长度则等于密钥长度。因此当加密内容长度大于密钥长度时，有效的RSA加解密就需要对内容进行分段。

这是因为，RSA算法本身要求加密内容也就是明文长度m必须0<m<密钥长度n。如果小于这个长度就需要进行padding，因为如果没有padding，就无法确定解密后内容的真实长度，字符串之类的内容问题还不大，以0作为结束符，但对二进制数据就很难，因为不确定后面的0是内容还是内容结束符。而只要用到padding，那么就要占用实际的明文长度，于是实际明文长度需要减去padding字节长度。我们一般使用的padding标准有NoPPadding、OAEPPadding、PKCS1Padding等，其中PKCS#1建议的padding就占用了11个字节。

这样，对于1024长度的密钥。128字节（1024bits）-减去11字节正好是117字节，但对于RSA加密来讲，padding也是参与加密的，所以，依然按照1024bits去理解，但实际的明文只有117字节了。

所以如果要对任意长度的数据进行加密，就需要将数据分段后进行逐一加密，并将结果进行拼接。同样，解码也需要分段解码，并将结果进行拼接。

Php实现

if (! function_exists('url_safe_base64_encode')) {
    function url_safe_base64_encode ($data) {
        return str_replace(array('+','/', '='),array('-','_', ''), base64_encode($data));
    }
}

if (! function_exists('url_safe_base64_decode')) {
    function url_safe_base64_decode ($data) {
        $base_64 = str_replace(array('-','_'),array('+','/'), $data);
        return base64_decode($base_64);
    }
}

class XRsa
{
    const CHAR_SET = "UTF-8";
    const BASE_64_FORMAT = "UrlSafeNoPadding";
    const RSA_ALGORITHM_KEY_TYPE = OPENSSL_KEYTYPE_RSA;
    const RSA_ALGORITHM_SIGN = OPENSSL_ALGO_SHA256;

    protected $public_key;
    protected $private_key;
    protected $key_len;

    public function __construct($pub_key, $pri_key = null)
    {
        $this->public_key = $pub_key;
        $this->private_key = $pri_key;

        $pub_id = openssl_get_publickey($this->public_key);
        $this->key_len = openssl_pkey_get_details($pub_id)['bits'];
    }

    /*
     * 创建密钥对
     */
    public static function createKeys($key_size = 2048)
    {
        $config = array(
            "private_key_bits" => $key_size,
            "private_key_type" => self::RSA_ALGORITHM_KEY_TYPE,
        );
        $res = openssl_pkey_new($config);
        openssl_pkey_export($res, $private_key);
        $public_key_detail = openssl_pkey_get_details($res);
        $public_key = $public_key_detail["key"];

        return [
            "public_key" => $public_key,
            "private_key" => $private_key,
        ];
    }

    /*
     * 公钥加密
     */
    public function publicEncrypt($data)
    {
        $encrypted = '';
        $part_len = $this->key_len / 8 - 11;
        $parts = str_split($data, $part_len);

        foreach ($parts as $part) {
            $encrypted_temp = '';
            openssl_public_encrypt($part, $encrypted_temp, $this->public_key);
            $encrypted .= $encrypted_temp;
        }

        return url_safe_base64_encode($encrypted);
    }

    /*
     * 私钥解密
     */
    public function privateDecrypt($encrypted)
    {
        $decrypted = "";
        $part_len = $this->key_len / 8;
        $base64_decoded = url_safe_base64_decode($encrypted);
        $parts = str_split($base64_decoded, $part_len);

        foreach ($parts as $part) {
            $decrypted_temp = '';
            openssl_private_decrypt($part, $decrypted_temp,$this->private_key);
            $decrypted .= $decrypted_temp;
        }
        return $decrypted;
    }

    /*
     * 私钥加密
     */
    public function privateEncrypt($data)
    {
        $encrypted = '';
        $part_len = $this->key_len / 8 - 11;
        $parts = str_split($data, $part_len);

        foreach ($parts as $part) {
            $encrypted_temp = '';
            openssl_private_encrypt($part, $encrypted_temp, $this->private_key);
            $encrypted .= $encrypted_temp;
        }

        return url_safe_base64_encode($encrypted);
    }

    /*
     * 公钥解密
     */
    public function publicDecrypt($encrypted)
    {
        $decrypted = "";
        $part_len = $this->key_len / 8;
        $base64_decoded = url_safe_base64_decode($encrypted);
        $parts = str_split($base64_decoded, $part_len);

        foreach ($parts as $part) {
            $decrypted_temp = '';
            openssl_public_decrypt($part, $decrypted_temp,$this->public_key);
            $decrypted .= $decrypted_temp;
        }
        return $decrypted;
    }

    /*
     * 数据加签
     */
    public function sign($data)
    {
        openssl_sign($data, $sign, $this->private_key, self::RSA_ALGORITHM_SIGN);

        return url_safe_base64_encode($sign);
    }

    /*
     * 数据签名验证
     */
    public function verify($data, $sign)
    {
        $pub_id = openssl_get_publickey($this->public_key);
        $res = openssl_verify($data, url_safe_base64_decode($sign), $pub_id, self::RSA_ALGORITHM_SIGN);

        return $res;
    }
}

Go实现

package xrsa

import (
    "encoding/pem"
    "encoding/base64"
    "crypto/x509"
    "crypto/rsa"
    "crypto/rand"
    "errors"
    "crypto"
    "io"
    "bytes"
    "encoding/asn1"
)

const (
    CHAR_SET = "UTF-8"
    BASE_64_FORMAT = "UrlSafeNoPadding"
    RSA_ALGORITHM_KEY_TYPE = "PKCS8"
    RSA_ALGORITHM_SIGN = crypto.SHA256
)

type XRsa struct {
    publicKey *rsa.PublicKey
    privateKey *rsa.PrivateKey
}

// 生成密钥对
func CreateKeys(publicKeyWriter, privateKeyWriter io.Writer, keyLength int) error {
    // 生成私钥文件
    privateKey, err := rsa.GenerateKey(rand.Reader, keyLength)
    if err != nil {
        return err
    }
    derStream := MarshalPKCS8PrivateKey(privateKey)
    block := &pem.Block{
        Type:  "PRIVATE KEY",
        Bytes: derStream,
    }
    err = pem.Encode(privateKeyWriter, block)
    if err != nil {
        return err
    }

    // 生成公钥文件
    publicKey := &privateKey.PublicKey
    derPkix, err := x509.MarshalPKIXPublicKey(publicKey)
    if err != nil {
        return err
    }
    block = &pem.Block{
        Type:  "PUBLIC KEY",
        Bytes: derPkix,
    }
    err = pem.Encode(publicKeyWriter, block)
    if err != nil {
        return err
    }

    return nil
}

func NewXRsa(publicKey []byte, privateKey []byte) (*XRsa, error) {
    block, _ := pem.Decode(publicKey)
    if block == nil {
        return nil, errors.New("public key error")
    }
    pubInterface, err := x509.ParsePKIXPublicKey(block.Bytes)
    if err != nil {
        return nil, err
    }
    pub := pubInterface.(*rsa.PublicKey)

    block, _ = pem.Decode(privateKey)
    if block == nil {
        return nil, errors.New("private key error!")
    }
    priv, err := x509.ParsePKCS8PrivateKey(block.Bytes)
    if err != nil {
        return nil, err
    }

    pri, ok := priv.(*rsa.PrivateKey)
    if ok {
        return &XRsa {
            publicKey: pub,
            privateKey: pri,
        }, nil
    } else {
        return nil, errors.New("private key not supported")
    }
}

// 公钥加密
func (r *XRsa) PublicEncrypt(data string) (string, error) {
    partLen := r.publicKey.N.BitLen() / 8 - 11
    chunks := split([]byte(data), partLen)

    buffer := bytes.NewBufferString("")
    for _, chunk := range chunks {
        bytes, err := rsa.EncryptPKCS1v15(rand.Reader, r.publicKey, chunk)
        if err != nil {
            return "", err
        }
        buffer.Write(bytes)
    }

    return base64.RawURLEncoding.EncodeToString(buffer.Bytes()), nil
}

// 私钥解密
func (r *XRsa) PrivateDecrypt(encrypted string) (string, error) {
    partLen := r.publicKey.N.BitLen() / 8
    raw, err := base64.RawURLEncoding.DecodeString(encrypted)
    chunks := split([]byte(raw), partLen)

    buffer := bytes.NewBufferString("")
    for _, chunk := range chunks {
        decrypted, err := rsa.DecryptPKCS1v15(rand.Reader, r.privateKey, chunk)
        if err != nil {
            return "", err
        }
        buffer.Write(decrypted)
    }

    return buffer.String(), err
}

// 数据加签
func (r *XRsa) Sign(data string) (string, error) {
    h := RSA_ALGORITHM_SIGN.New()
    h.Write([]byte(data))
    hashed := h.Sum(nil)

    sign, err := rsa.SignPKCS1v15(rand.Reader, r.privateKey, RSA_ALGORITHM_SIGN, hashed)
    if err != nil {
        return "", err
    }
    return base64.RawURLEncoding.EncodeToString(sign), err
}

// 数据验签
func (r *XRsa) Verify(data string, sign string) error {
    h := RSA_ALGORITHM_SIGN.New()
    h.Write([]byte(data))
    hashed := h.Sum(nil)

    decodedSign, err := base64.RawURLEncoding.DecodeString(sign)
    if err != nil {
        return err
    }

    return rsa.VerifyPKCS1v15(r.publicKey, RSA_ALGORITHM_SIGN, hashed, decodedSign)
}

func MarshalPKCS8PrivateKey(key *rsa.PrivateKey) []byte {
    info := struct {
        Version             int
        PrivateKeyAlgorithm []asn1.ObjectIdentifier
        PrivateKey          []byte
    }{}
    info.Version = 0
    info.PrivateKeyAlgorithm = make([]asn1.ObjectIdentifier, 1)
    info.PrivateKeyAlgorithm[0] = asn1.ObjectIdentifier{1, 2, 840, 113549, 1, 1, 1}
    info.PrivateKey = x509.MarshalPKCS1PrivateKey(key)

    k, _ := asn1.Marshal(info)
    return k
}

func split(buf []byte, lim int) [][]byte {
    var chunk []byte
    chunks := make([][]byte, 0, len(buf)/lim+1)
    for len(buf) >= lim {
        chunk, buf = buf[:lim], buf[lim:]
        chunks = append(chunks, chunk)
    }
    if len(buf) > 0 {
        chunks = append(chunks, buf[:len(buf)])
    }
    return chunks
}

Java实现

package com.inspii;

import org.apache.commons.codec.binary.Base64;
import org.apache.commons.io.IOUtils;

import javax.crypto.Cipher;
import java.io.ByteArrayOutputStream;
import java.security.*;
import java.security.interfaces.RSAPublicKey;
import java.security.interfaces.RSAPrivateKey;
import java.security.spec.PKCS8EncodedKeySpec;
import java.security.spec.X509EncodedKeySpec;
import java.util.HashMap;
import java.util.Map;

public class XRsa {
    public static final String CHARSET = "UTF-8";
    public static final String RSA_ALGORITHM = "RSA";
    public static final String RSA_ALGORITHM_SIGN = "SHA256WithRSA";

    private RSAPublicKey publicKey;
    private RSAPrivateKey privateKey;

    public XRsa(String publicKey, String privateKey)
    {
        try {
            KeyFactory keyFactory = KeyFactory.getInstance(RSA_ALGORITHM);

            //通过X509编码的Key指令获得公钥对象
            X509EncodedKeySpec x509KeySpec = new X509EncodedKeySpec(Base64.decodeBase64(publicKey));
            this.publicKey = (RSAPublicKey) keyFactory.generatePublic(x509KeySpec);
            //通过PKCS#8编码的Key指令获得私钥对象
            PKCS8EncodedKeySpec pkcs8KeySpec = new PKCS8EncodedKeySpec(Base64.decodeBase64(privateKey));
            this.privateKey = (RSAPrivateKey) keyFactory.generatePrivate(pkcs8KeySpec);
        } catch (Exception e) {
            throw new RuntimeException("不支持的密钥", e);
        }
    }

    public static Map<String, String> createKeys(int keySize){
        //为RSA算法创建一个KeyPairGenerator对象
        KeyPairGenerator kpg;
        try{
            kpg = KeyPairGenerator.getInstance(RSA_ALGORITHM);
        }catch(NoSuchAlgorithmException e){
            throw new IllegalArgumentException("No such algorithm-->[" + RSA_ALGORITHM + "]");
        }

        //初始化KeyPairGenerator对象,不要被initialize()源码表面上欺骗,其实这里声明的size是生效的
        kpg.initialize(keySize);
        //生成密匙对
        KeyPair keyPair = kpg.generateKeyPair();
        //得到公钥
        Key publicKey = keyPair.getPublic();
        String publicKeyStr = Base64.encodeBase64URLSafeString(publicKey.getEncoded());
        //得到私钥
        Key privateKey = keyPair.getPrivate();
        String privateKeyStr = Base64.encodeBase64URLSafeString(privateKey.getEncoded());
        Map<String, String> keyPairMap = new HashMap<String, String>();
        keyPairMap.put("publicKey", publicKeyStr);
        keyPairMap.put("privateKey", privateKeyStr);

        return keyPairMap;
    }

    public String publicEncrypt(String data){
        try{
            Cipher cipher = Cipher.getInstance(RSA_ALGORITHM);
            cipher.init(Cipher.ENCRYPT_MODE, publicKey);
            return Base64.encodeBase64URLSafeString(rsaSplitCodec(cipher, Cipher.ENCRYPT_MODE, data.getBytes(CHARSET), publicKey.getModulus().bitLength()));
        }catch(Exception e){
            throw new RuntimeException("加密字符串[" + data + "]时遇到异常", e);
        }
    }

    public String privateDecrypt(String data){
        try{
            Cipher cipher = Cipher.getInstance(RSA_ALGORITHM);
            cipher.init(Cipher.DECRYPT_MODE, privateKey);
            return new String(rsaSplitCodec(cipher, Cipher.DECRYPT_MODE, Base64.decodeBase64(data), publicKey.getModulus().bitLength()), CHARSET);
        }catch(Exception e){
            throw new RuntimeException("解密字符串[" + data + "]时遇到异常", e);
        }
    }

    public String privateEncrypt(String data){
        try{
            Cipher cipher = Cipher.getInstance(RSA_ALGORITHM);
            cipher.init(Cipher.ENCRYPT_MODE, privateKey);
            return Base64.encodeBase64URLSafeString(rsaSplitCodec(cipher, Cipher.ENCRYPT_MODE, data.getBytes(CHARSET), publicKey.getModulus().bitLength()));
        }catch(Exception e){
            throw new RuntimeException("加密字符串[" + data + "]时遇到异常", e);
        }
    }

    public String publicDecrypt(String data){
        try{
            Cipher cipher = Cipher.getInstance(RSA_ALGORITHM);
            cipher.init(Cipher.DECRYPT_MODE, publicKey);
            return new String(rsaSplitCodec(cipher, Cipher.DECRYPT_MODE, Base64.decodeBase64(data), publicKey.getModulus().bitLength()), CHARSET);
        }catch(Exception e){
            throw new RuntimeException("解密字符串[" + data + "]时遇到异常", e);
        }
    }

    public String sign(String data){
        try{
            //sign
            Signature signature = Signature.getInstance(RSA_ALGORITHM_SIGN);
            signature.initSign(privateKey);
            signature.update(data.getBytes(CHARSET));
            return Base64.encodeBase64URLSafeString(signature.sign());
        }catch(Exception e){
            throw new RuntimeException("签名字符串[" + data + "]时遇到异常", e);
        }
    }

    public boolean verify(String data, String sign){
        try{
            Signature signature = Signature.getInstance(RSA_ALGORITHM_SIGN);
            signature.initVerify(publicKey);
            signature.update(data.getBytes(CHARSET));
            return signature.verify(Base64.decodeBase64(sign));
        }catch(Exception e){
            throw new RuntimeException("验签字符串[" + data + "]时遇到异常", e);
        }
    }

    private static byte[] rsaSplitCodec(Cipher cipher, int opmode, byte[] datas, int keySize){
        int maxBlock = 0;
        if(opmode == Cipher.DECRYPT_MODE){
            maxBlock = keySize / 8;
        }else{
            maxBlock = keySize / 8 - 11;
        }
        ByteArrayOutputStream out = new ByteArrayOutputStream();
        int offSet = 0;
        byte[] buff;
        int i = 0;
        try{
            while(datas.length > offSet){
                if(datas.length-offSet > maxBlock){
                    buff = cipher.doFinal(datas, offSet, maxBlock);
                }else{
                    buff = cipher.doFinal(datas, offSet, datas.length-offSet);
                }
                out.write(buff, 0, buff.length);
                i++;
                offSet = i * maxBlock;
            }
        }catch(Exception e){
            throw new RuntimeException("加解密阀值为["+maxBlock+"]的数据时发生异常", e);
        }
        byte[] resultDatas = out.toByteArray();
        IOUtils.closeQuietly(out);
        return resultDatas;
    }
}

参考

github地址： https://github.com/liamylian/…